Wheel A of radius ra = 14.6 cm is coupled by belt B to wheel C of radius rc = 30.2 cm. Wheel A increases its angular speed from rest at time t = 0 s at a uniform rate of 5.0 rad/s2. At what time will wheel C reach a rotational speed of 52.9 rev/min, assuming the belt does not slip?

Answer 1

Both wheels have the same linear speed
v=ω1•r1= ω2•r2
Taking into account that
ω1=ε•t,
ω2= 2•π•n=(2•π•52.9)/60 (rad/s)
ε•t•r1=(2•π•52.9/60)•r2

t= (ω2•r2)/ε•r1=(ω2•r2)/(2•π•52.9/60)•r2 =2.29 s.

Answer 2

thank you!